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The model implied by factor score predictors does not reproduce thenon-diagonal elements of the observed covariance matrix as well as the factorloadings. It is therefore investigated whether it is possible to estimatefactor loadings for which the model implied by the factor score predictorsoptimally reproduces the non-diagonal elements of the observed covariancematrix. Accordingly, loading estimates are proposed for which the model impliedby the factor score predictors allows for a least-squares approximation of thenon-diagonal elements of the observed covariance matrix. This estimation methodis termed Score predictor factor analysis and algebraically compared withMinres factor analysis as well as principal component analysis. A populationbased and a sample based simulation study was performed in order to compareScore predictor factor analysis, Minres factor analysis, and principalcomponent analysis. It turns out that the non-diagonal elements of the observedcovariance matrix can more exactly be reproduced from the factor scorepredictors computed from Score predictor factor analysis than from the factorscore predictors computed from Minres factor analysis and from principalcomponents. Moreover, Score predictor factor analysis can be helpful toidentify factors when the factor model does not perfectly fit to the databecause of model error.

Score predictor factor analysis: Reproducing observed covariances by means of factor score predictors